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Example: as shown in the following figure of Floyd's triangle, 25 is a centered square number, and is the sum of the square 16 (yellow rhombus formed by shearing a square) and of the next smaller square, 9 (sum of two blue triangles): Centered square numbers (in red) are in the center of odd rows of Floyd's triangle.
Introduced in Python 2.2 as an optional feature and finalized in version 2.3, generators are Python's mechanism for lazy evaluation of a function that would otherwise return a space-prohibitive or computationally intensive list. This is an example to lazily generate the prime numbers:
which is both the t-th triangular number and the s-th square number. A near-isosceles Pythagorean triple is an integer solution to a 2 + b 2 = c 2 where a + 1 = b. The next table shows that splitting the odd number H n into nearly equal halves gives a square triangular number when n is even and a near isosceles Pythagorean triple when n is odd ...
push 1L (the number one with type long) onto the stack ldc 12 0001 0010 1: index → value push a constant #index from a constant pool (String, int, float, Class, java.lang.invoke.MethodType, java.lang.invoke.MethodHandle, or a dynamically-computed constant) onto the stack ldc_w 13 0001 0011 2: indexbyte1, indexbyte2 → value
An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
The examples below implement the perfect digital invariant function for = and a default base = described in the definition of happy given at the top of this article, repeatedly; after each time, they check for both halt conditions: reaching 1, and repeating a number. A simple test in Python to check if a number is happy:
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
1624 = number of squares in the Aztec diamond of order 28 [366] 1625 = centered square number [14] 1626 = centered pentagonal number [46] 1627 = prime and 2 × 1627 - 1 = 3253 is also prime [367] 1628 = centered pentagonal number [46] 1629 = rounded volume of a regular tetrahedron with edge length 24 [289] 1630 = number k such that k^64 + 1 is ...